<p>The conventional loosely bound molecule interpretation of the <i>X</i>(3872) is not compatible with the recent LHCb experimental measurement of the ratio of branching fractions <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25878_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">R</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{R} \)</EquationSource> </InlineEquation> = Br(<i>X</i> → <i>ψ</i>′<i>γ</i>)<i>/</i>Br(<i>X</i> → <i>ψγ</i>). We systematically determine the entire tetraquark spectrum for <i>J</i> = 0<i>,</i> 1<i>,</i> 2 and refine the calculation of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25878_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">R</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{R} \)</EquationSource> </InlineEquation> in an improved Born-Oppenheimer description of the <i>X</i>(3872) compact tetraquark. This refinement yields a significantly better agreement with experimental data on <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25878_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">R</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{R} \)</EquationSource> </InlineEquation> and on the spectroscopy of the states themselves. Extending the diquark-antidiquark paradigm to encompass tetraquarks that are linear super-positions of open charm singlets and color octets, we discover that these exotic resonances manifest as compact shallow bound states of quarks in color force potentials.</p>

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Tetraquarks in the Born-Oppenheimer approximation

  • D. Germani,
  • B. Grinstein,
  • A. D. Polosa

摘要

The conventional loosely bound molecule interpretation of the X(3872) is not compatible with the recent LHCb experimental measurement of the ratio of branching fractions R \( \mathcal{R} \) = Br(Xψγ)/Br(Xψγ). We systematically determine the entire tetraquark spectrum for J = 0, 1, 2 and refine the calculation of R \( \mathcal{R} \) in an improved Born-Oppenheimer description of the X(3872) compact tetraquark. This refinement yields a significantly better agreement with experimental data on R \( \mathcal{R} \) and on the spectroscopy of the states themselves. Extending the diquark-antidiquark paradigm to encompass tetraquarks that are linear super-positions of open charm singlets and color octets, we discover that these exotic resonances manifest as compact shallow bound states of quarks in color force potentials.